Communications in Mathematical Sciences
Volume 17 (2019)
Asymptotic traveling wave for a pricing model with multiple credit rating migration risk
Pages: 1975 – 2004
In this paper, an asymptotic traveling wave of a free boundary problem related to a pricing model for corporate bond with multiple credit rating migration risk is studied. The pricing model is captured by a free boundary problem, whose existence, uniqueness and regularity of the solution are obtained such that the rationality of the model is guaranteed. The existence of a unique traveling wave in the free boundary problem is established with some risk discount rate condition satisfied. The inductive method is applied to overcome the multiplicity of free boundaries. We prove that the solution of the pricing model for corporate bond is convergent to the traveling wave, which shows a clear dynamics of price change for the corporate bond.
traveling wave, asymptotic behavior, free boundary problem, multiple credit rating migration, pricing model for corporate bond
2010 Mathematics Subject Classification
35K10, 60H10, 91G40
This work was supported by the National Natural Science Foundation (No. 11701115).
Received 22 January 2019
Accepted 1 July 2019
Published 6 January 2020